2 Answers
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When combining diet and weight loss, it's important to decide how you are going to measure progress.

Your reasoning is correct. The scale will move more slowly when you are getting stronger while losing weight. You may even lose fat and gain weight!

There are some obvious qualifiers for that statement:

This all depends on your starting point.

People with low muscular development will build muscle much quicker than people with moderate or advanced muscular development.

The rate of fat loss depends on how much excess fat you have.

If you look at some of the body transformations on Fitocracy, you will find a number of women who actually added weight while their clothes fit better and looked thinner. Naturally, if you have a lot of fat to loose, you will lose weight before you are done.

Revised Goals

Focus on fat loss. The scale may or may not move the way you want in any given week and you didn't cheat once. However, you might notice your clothes getting looser.

Take regular measurements. Measure the size of your neck, arms, chest, abs, hips, legs weekly. You should be losing inches over time, and the fattier parts of you should be getting firmer. This is your #1 check to make sure what you are doing is working.

Take quarterly progress pictures. Even 1 month is too soon to really see how progress is going, but after 3 months you should see some differences.

The scale is a useful tool while loosing weight, but if it starts increasing and your clothes are fitting better, that means you've put on more muscle than you've lost fat. If the scale is reading the same number, then the exchange is about the same. If the scale is going down, then you are losing more fat than gaining muscle.

Fat loss is not linear

You may find some weeks where the fat seems to melt off, and then several weeks where it seems like you're never going to lose the fat. That's why I recommend having more than one way to measure progress. You'll also find that scales that report the body fat percentage are not that accurate. It's easy to get depressed looking at the scale's numbers when the inches you've lost tell the real story.

As you get leaner, you will have to adjust your diet to keep progressing. That's because as you lose overall mass your metabolic rate will drop because it doesn't have to support all the extra fat. That means the number of calories you needed to maintain the physical activity and lose weight will get lower over time. That's expected, and you'll have to recalculate your requirements every 5-10 pounds you lose.

Weight is just a number it should not be a goal to make the needle move less when you step on it unless you're obese. Even then, in order to lose weight you have to burn calories. Weight lifting is a good additional activity to burns calories.

Should you loose fat and gain so much muscle that your weight increases, you're sitting on every body builder's dream. I can almost promise that this will not happen w/o unnatural assistance.

Another fact is that the more muscle you have, the more calories you burn while performing daily tasks. This is why it gets progressively more difficult for some people to add muscle when that is desirable.

As much as we may desire change, the human body tries to remain the same or change slowly. This is why people as they get bigger get stretch marks (from muscle or fat). Similarly when you lose weight quickly, you'll have extra "skin" until your body reclaims it. We can't let our minds be disappointed in the limitations that EVERY body has.